In food processor or blender, place garlic cloves, red onion, jalapeno pepper, parsley, cilantro, salt, cumin, oregano, orange juice and vegetable oil. Puree thoroughly. Set marinade aside. Gently insert fingers under skin, loosening as much as possible without puncturing over breast, thighs and drumsticks. Place chicken in plastic oven roasting bag. Rub marinade into meat beneath the loosened skin and into body and neck cavities. Place quartered orange and quartered onion pieces inside body cavity. Pour any remaining marinade over chicken and close bag tightly. Refrigerate overnight. Remove chicken from marinade and pat dry.
Grill chicken over charcoal (or gas - medium heat) medium-hot coals until skin is deep golden brown and meat is cooked through, about 1 hour and 40 minutes (or about 25 minutes per pound.) Internal temperature should reach 180ºF when done, measured in the deepest part of the thigh, not touching the bone. (Or, roast chicken 90 minutes at 375ºF.)
While chicken cooks, prepare Starfruit Cranberry Sauce by combining orange juice and sugar in heavy saucepan. Bring to a boil over medium-high heat, stirring. Reduce heat to simmer; cook 5 minutes. Stir in starfruit, cranberries and ginger. Simmer, stirring, until berries pop, about 8 minutes. Set aside to cool. Serve chilled or at room temperature.